Aroller coaster car (mass = m) is on a track that forms a circular loop (radius = r) in the vertical plane. if the car is to just maintain contact with the track at the top of the loop, what is the minimum value for its speed at that point?

Asmall grinding wheel has a moment of inertia of 4.0×10−5 kg⋅m2 . what net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2 ?

It may seem strange that the selected velocity does not depend on either the mass or the charge of the particle. (for example, would the velocity of a neutral particle be selected by passage through this device? ) the explanation of this is that the mass and the charge control the resolution of the device--particles with the wrong velocity will be accelerated away from the straight line and will not pass through the exit slit. if the acceleration depends strongly on the velocity, then particles with just slightly wrong velocities will feel a substantial transverse acceleration and will not exit the selector. because the acc

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?